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What is the bulk modulus of a material if a pressure increase of 50 MPa results

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Question: What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)

Options:

  1. 25 GPa
  2. 50 GPa
  3. 100 GPa
  4. 200 GPa

Correct Answer: 50 GPa

Exam Year: 2022

Solution: 

Bulk modulus (K) = -ΔP / (ΔV/V) = -50 MPa / (-0.002 m³ / 1 m³) = 25000 MPa = 25 GPa.

What is the bulk modulus of a material if a pressure increase of 50 MPa results

Practice Questions

Q1
What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)
  1. 25 GPa
  2. 50 GPa
  3. 100 GPa
  4. 200 GPa

Questions & Step-by-Step Solutions

What is the bulk modulus of a material if a pressure increase of 50 MPa results in a volume decrease of 0.002 m³ for a volume of 1 m³? (2022)
  • Step 1: Understand the formula for bulk modulus (K), which is K = -ΔP / (ΔV/V). Here, ΔP is the change in pressure, ΔV is the change in volume, and V is the original volume.
  • Step 2: Identify the values given in the question. We have ΔP = 50 MPa (pressure increase) and ΔV = -0.002 m³ (volume decrease). The original volume V = 1 m³.
  • Step 3: Calculate the ratio ΔV/V. This is done by dividing the change in volume by the original volume: ΔV/V = -0.002 m³ / 1 m³ = -0.002.
  • Step 4: Substitute the values into the bulk modulus formula: K = -ΔP / (ΔV/V) = -50 MPa / (-0.002).
  • Step 5: Perform the calculation: K = 50 MPa / 0.002 = 25000 MPa.
  • Step 6: Convert the result from MPa to GPa. Since 1 GPa = 1000 MPa, we divide by 1000: 25000 MPa = 25 GPa.
  • Bulk Modulus – The bulk modulus is a measure of a material's resistance to uniform compression, defined as the ratio of pressure increase to the relative decrease in volume.
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